Buckling-Path Generative Modeling: A Mechanism-Guided Framework for Three-Dimensional Shape Synthesis Through Bending, Mechanical Instability, and Morphological Transitions

Three-dimensional generative models commonly represent shape synthesis as the prediction of geometric primitives, implicit fields, point distributions, or latent geometric representations. Although these approaches can generate visually plausible objects, the processes responsible for producing mechanically induced shapes are not necessarily represented explicitly. This paper proposes Buckling-Path Generative Modeling (BPGM), a mechanism-guided framework for three-dimensional shape synthesis in which geometry emerges through learned sequences of bending, compression, instability, and morphological transitions. Rather than treating the final shape as the sole generative target, BPGM models a path through a space of mechanically conditioned configurations. Its proposed architecture consists of an initial-geometry encoder, a mechanical-condition encoder, a candidate-instability generator, a mode-selection controller, a deformation integrator, and a geometry decoder. The controller selects among competing deformation modes according to learned geometric compatibility, predicted mechanical response, target-shape relevance, and transition cost. A path-dependent objective combines geometric reconstruction, mechanical consistency, transition regularization, mode diversity, and terminal-shape agreement. The framework can be instantiated with meshes, point clouds, signed distance fields, or other compatible three-dimensional representations. A research protocol is specified for evaluating BPGM against direct geometry generation, conventional deformation models, and physics-guided generative baselines. The proposed method is a conceptual framework rather than an experimentally validated system. Its central research hypothesis is that explicitly modeling the selection and progression of instability modes may improve controllability and structural interpretability in three-dimensional generation tasks involving thin sheets, compressed structures, buckling patterns, and mechanically induced shape transitions.